The Hammers had Mark Noble's 76th-minute penalty to thank for the victory in East London - their seventh in a row over the Tigers - which sends them up to 13th place
Andre Ayew's West Ham United have overcome rock bottom Hull City 1-0 to pick up their first back-to-back Premier League wins at their London Stadium home.
The Hammers had Mark Noble's 76th-minute penalty to thank for the victory in East London - their seventh in a row over the Tigers - which sends them up to 13th place.
Hull drop to the foot of the table, meanwhile, with their seventh away defeat on the spin in the top flight enough to equal an unwanted club record under Mike Phelan.
United continued to ride their luck as eventual matchwinner Noble headed against his own post from Andrew Robertson's dangerous cross, before the Scottish wing-back smashed a shot against the post.
Hull's failure to convert would cost them dearly, but only after both Andre Ayew and Michael Dawson had attempts kept off the line for their respective sides in an explosive five-minute spell.
Carroll headed into the arms of David Marshall as the second half transpired and Robert Snodgrass picked out the roof of the net with his latest shot, but the decisive moment arrived 75 minutes in after Tom Huddlestone fouled Michail Antonio inside the box.
Three days after missing from the spot against Burnley, before converting the rebound, Noble made no mistake this time as he sent Marshall the wrong way.
Marshall kept out a Dimitri Payet drive late on, while Maguire also shot too close to Randolph, as the Hammers held on to claim three valuable points to climb up the table.